Question

Look at image shown simplify expression and write answer without negative exponents please

Answer 1

Answer:

The expression without a negative exponent will be:

$\frac{8x^{-4}y^{-8}}{-2xy^5}=-\frac{4}{x^5y^{13}}$        

Step-by-step explanation:

Given the function

$\frac{8x^{-4}\:y^{-8}}{-2xy^5}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}$

$\frac{8x^{-4}\:y^{-8}}{-2xy^5}=-\frac{8x^{-4}y^{-8}}{2xy^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4$

               $=-\frac{4x^{-4}y^{-8}}{xy^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}$

                $=-\frac{4y^{-8}}{x^5y^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}$

  i.e.   $\frac{y^{-8}}{y^5}=\frac{1}{y^{5-\left(-8\right)}}$

so the expression becomes

    $\frac{8x^{-4}\:y^{-8}}{-2xy^5}=-\frac{4}{x^5y^{5-\left(-8\right)}}$      

                  $=-\frac{4}{x^5y^{13}}$

Therefore, the expression without a negative exponent will be:

$\frac{8x^{-4}y^{-8}}{-2xy^5}=-\frac{4}{x^5y^{13}}$